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Scalar and Vector Operations

Moment of inertia of a system of masses.

An object is made up of three masses connected by massless rods of fixed length. Mass A is located at (30.0 cm, 0 cm) and has a mass of 250 grams, mass B is located at (0 cm, 30.0 cm) and has a mass of 350 grams, mass C is located at (-30.0 cm, 0 cm) and has a mass of 450 grams. What is the moment of inertia of this object about

Eigenvalues, eigenvectors, and time evolution.

Dear Mitra, I in fact wrote the wrong matrix but I am still confused after PART A. (PART A) The actual matrix is: H = 1 2 0 2 0 2 0 2 -1 Where the eigenvalues are E1 =0, E2=3hw, E3=-3hw and as you said the trace(H) =0 = sum of eigenvalues. I also found the eigenvectors using Hx = Ex and they w

Westward component

A soccer player carries the ball for a distance of 40.0 m in the direction 42.0 west of south. Find the westward component of the ball's displacement. 26.8 m 29.7 m 36.0 m None of the other choices is correct.

orthogonality condition is preserved under orthogonal transform

Part i) Show that if u & v are orthogonal, then the transformed vectors U = Au & V = Av under the linear (orthogonal) transformation (characterised by the orthogonal matrix A) are themselves orthogonal. I think this can be done using pythagoras theorem but am not sure how to begin, please help! Part ii) shSw that the orthogon

Problems involving scalar and vector operations

The eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements is correct for these two vectors? Choices: Vector A is parallel to vector B Vector A is anti-parallel to vector B The magnitude of vector A is equal to the mag

Direction relative to ground

A plane has an airspeed of 142 m/s. A 30 m/s wind is blowing southward at the same time as the plane is flying. What must be the direction of the plane in order to move due east relative to the ground? Answer choices: 78.1 degrees north of east 11.9 degrees north of east 77.8 degrees north of east 12.2 degrees north of

Adding Vectors

Vector A=6 m and points 30 degrees south of east. Vector B=4 m and points 30 degrees south of west. Find the resultant vector A+B. Answer Choices: 3.3 m at an angle of 71 degrees south of east. 5.3 m at an angle of 71 degrees south of east 3.3 m at an angle of 19 degrees south of east 5.3 m at an angle of 19 degrees sou

The answer to Resultant Force

Three forces are acting on the origin. F1 has a magnitude of 70 N and is 30 degrees north of east. F2 has a magnitude of 70 N and is 30 degrees north of west. F3 has a magnitude of 70 N and is along the south direction. Find the resultant force acting on the origin.

Vector Transformation for Spatial Coordinate Systems

Consider a two-dimensional spatial coordinate system S' whose coordinates (u,v) are defined by x = u + v y = u - v in terms of the coordinates of a Cartesian coordinate system S. Suppose you are given a vector in S whose contravariant components are Am = (2,8). Determine the contravariant components of this ve

Velocity of a charge moving in a magnetic field

The problem states: A particle with a charge of -5.90 * 10^-9 C is moving in a uniform magnetic field B(vector) = -(1.25 T) k (hat). The magnetic force on the particle is measured to be F(vector) = -(4.00 * 10^-7 N) i(hat) + (7.60 * 10^-7 N) j(hat). 1. Are there components of the velocity that are not determined by the

Vectors and Unit Vector

The vector A has a magnitude of 3.00 meters. It makes an angle of 30° with respect to the positive x-axis. The vector B has a magnitude of 3.00 meters, but points along the y-axis. What are the horizontal and vertical components of ? a) Ax = 2.60, Ay = 1.50 b) Ax = 1.50, Ay = 2.60 c) Ax = 3.00, Ay = 3.00 d) Ax = -2.

Vector problem

So here is the question Let A= {10, 30°} be a vector of magnitude 10 ( in some units) and pointing in a direction of 30°counter-clockwise from positive x. Let B = { 7, 225°degree} Find x and Y componens of these two vectors A { AX= AY= B { Bx= BY= Find x and y components of the sum S= A+B S= { Sx= S

Resultant Vectors of 3 Displacement Vectors

How do I find the resultant of the three displacement vectors in the drawing by means of the component method? If the magnitudes of the vectors are A= 5 m B=5 m and C= 4 m?

Magnitude of Displacement Vector

An ocean liner leaves New York and travels 18.0 degrees north of east for 155 km. How far east and how far north has it gone? How do I figure out the magnitudes of the ships displacement vector in the directions due east and due north?

Magnitude and Direction of a Resultant Vector

If Displacement vector A points due east and has a magnitude of 2.00 km. Displacement vector B points due north and has a magnitude of 3.75 km. Displacement vector C points due west and has a magnitude of 2.50 km. Displacement vector D points due south and has a magnitude of 3.00 km. How can I find the magnitude and direction (

Pair of forces

Consider a pair of forces, one having a magnitude of 20 N, and the other having a magnitude of 12 N. What maximum net force is possible for these two forces? What is the minimum net force possible?

electric field and potential of point like charges.

(See attached file for full problem description) --- Two equal, positive charges, q = 2.0 micro Coulomb ; are located on the x-axis- one at +0.3m and the other at -0.3m. A third charge Q = +4.0 micro Coulomb is located on the y-axis at +0.4m 1) Find the magnitude & direction of the resultant (net) force on Q. 2) Find

Stokes and Gauss' Theorem

1. A vector field v(x, y, z) is given by the formula v(x, y, z) = xyˆx − yˆ2y. Consider a square path in the xy plane which starts at (0,0,0) and moves along the corners (1,0,0), (1,1,0) and (0,1,0). Calculate the path integral of v, i.e. v · dr, and calculate the area integral of the divergence, R ∇ × v · da, an

Center of Mass of Particles

A) Find the xcm coordinate of the center of mass of the system of particles shown in the figure. (See attached file for full problem description with diagram and values) Express your answer in meters to two significant figures. xcm = B) A straight rod has one end at the origin and the other end at the point (L,0) and

Center of Mass and Coordinate System

A system of four buckets forms a square as shown in the figure. Initially, the buckets have different masses (it is not known how these masses are related). A student begins to add water gradually to the bucket located at the origin. As a result, what happens to the coordinates of the center of mass of the system of buckets? (Se

Find the x coordinate of the center of mass.

Please see the attached file for full problem description with diagram. For the system of particles described above, find the x coordinate xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right. Express your answer in terms of L.

Force; Calculating X and Y Components of a Quadrant

Could you show me how to perform the calculation asked for? It is part B. Calculate the theoretical x and y components of the first quadrant force vector using the cosine and sine of the measured angle and the measured first quadrant force. Then compare these values to the experimental scale readings along the x and y directi

Scalar and Vector Operations

(See attached file for full problem description with proper symbols) 1. Write each vector in terms of the unit vectors ^i and ^j. 2. Use unit vectors to express the vector C, where C = 3.00A - 4.00B. 3. Find the magnitude and direction of C.

Direction and Work Done by Electric Field

(See attached file for full problem description) --- 4 a) Sketch arrows on the diagram (see attachment) to indicate the direction of the electric field, if any, at each of the points A, B, C, and D. A positively charged test particle is observed to move as described below. For each motion, tell whether the work done by

Vector Addition and Visual Representation

1) Find the angle that the vector makes with vector . Express in terms of and any of the quantities given in the problem introduction ( , , and/or ) as well as any necessary constants. 2) In the coordinate system, what are the components of ? Express your answer as an ordered pair separated by a comma. Give your

Vector Cross Product

The vector is 3.50 cm long and is directed into this page. Vector points from the lower-right corner of this page to the upper-left corner of this page and has the components , . 1) In the right-handed coordinate system, where the +x-axis directed to the right, the +y-axis toward the top of the page, and +z-axis out of th

Vector calculation of a plane

A plane leaves the airport in Galisto and flies a distance 170 km at an angle 68.0 degree east of north and then changes direction to fly a distance 270 km at an angle 48.0 degree south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, how far should this crew